Question

Can someone please help me with these two questions??

2. 0/2 points Previous Answers WaneFMAC7 6.3.004. Maximize p = 2x + 3y subject to 3x + By S51 6x + 4y 5 48 x 20 y 20. (XY) - ( Need Help? Read Watch Submit Answer Practice Another Version

Answer 1

2) 3x + 8y $\leq$ 51

So, multiplying with 2 we get

6x + 16y $\leq$ 102

Also 6x +4y $\leq$ 48

Subtracting above two equations we get

12y $\leq$ 54

y $\leq$ 4.5

Also 6x + 4(4.5) $\leq$ 48

6x $\leq$ 48- 18 = 30

x $\leq$ 30/6 = 5

P = 2(5) + 3(4.5) = 23.5

so, answer is

p = 23.5

(X,Y) = (3,4.5)

3) 2x + y $\geq$ 80

y + z $\geq$80

Adding both we get

2x + 2y +z $\geq$160 (1)

Also x + y + z $\geq$ 90

So, 2x +2y +2z $\geq$180 (2)

Subtracting (1) from (2), we get

z $\geq$ 20

So, y + 20 $\geq$ 80

y $\geq$ 60

And 2x + 60 $\geq$80

2x $\geq$ 20

x $\geq$ 10

Hence c = 3(10) + 60 + 5(20) = 30+60+100 = 190

Answer is

c = 190

(x,y,z) = (10,60,20)